Abstract

This paper describes a parametric approach to weakening rationality assumptions in game theory to fit empirical data better. The central features of game theory are: The concept of a game (players, strategies, information, timing, outcomes); strategic thinking; mutual consistency of beliefs and strategies; and strategic foresight and Bayesian updating of unobserved "types" in repeated games. This paper describes a general four-parameter behavioral approach which relaxes the mutual consistency and foresight properties, while retaining much of the structure and hence the precision of game theory. One parameter measures the number of steps of iterated thinking that the average player does. This "thinking steps" model generates predictions about one-shot games and provides initial conditions for a theory of learning in repeated games. The learning theory adds one parameter (to measure response sensitivity) and adjusts learning parameters for environmental change (e.g., old experience is rapidly decayed when other players' moves are changing). It predicts behavior in new games more accurately than comparable models like fictitious play and reinforcement learning. The teaching theory assumes some fraction of players realize the impact of their current choices on future behavior of other players who learn, but does not impose equilibrium or updating assumptions as in standard approaches. The thinking-learning-teaching model is fit to many experimental data sets (a total of several thousand observations) including entry, mixed-equilibrium, "beauty contest", coordination, matrix games, and repeated trust games with incomplete information.

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